Efficient on-line schemes for encoding individual sequences with side information at the decoder

We present adaptive on-line schemes for lossy encoding of individual sequences, under the conditions of the Wyner-Ziv (WZ) problem, i.e., the decoder has access to side information whose statistical dependency on the source is known. Both the source sequence and the side information consist of symbols taking on values in a finite alphabet X. A set of fixed-rate scalar source codes with zero delay is presented. We propose a randomized on-line coding scheme, which achieves asymptotically (and with high probability), the performance of the best source code in the set, uniformly over all source sequences. The scheme uses the same rate and has zero delay.We then present an efficient algorithm for implementing our on-line coding scheme in the case of a relatively small set of encoders. We also present an efficient algorithm for the case of a larger set of encoders with a structure, using the method of the weighted graph and the Weight Pushing Algorithm (WPA). The complexity of these algorithms is no more than linear in the sequence length.